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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 480240ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480240.ch1 | 480240ch1 | \([0, 0, 0, -5763, 167362]\) | \(7088952961/50025\) | \(149373849600\) | \([2]\) | \(1048576\) | \(0.97681\) | \(\Gamma_0(N)\)-optimal |
480240.ch2 | 480240ch2 | \([0, 0, 0, -2163, 374002]\) | \(-374805361/20020005\) | \(-59779414609920\) | \([2]\) | \(2097152\) | \(1.3234\) |
Rank
sage: E.rank()
The elliptic curves in class 480240ch have rank \(1\).
Complex multiplication
The elliptic curves in class 480240ch do not have complex multiplication.Modular form 480240.2.a.ch
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.